Method and apparatus for an electromagnetic propulsion system

ABSTRACT

A method and apparatus to amplify the magnetic field in an electromagnetic circuit is provided. Amplification factors of several orders of magnitude may be obtained. The system is applicable to a number of different systems, including melt levitation and electromagnetic pumping and propulsion. One embodiment of the invention uses a non-conducting permeable core wound around a dielectric core. An alternating voltage source is connected to a solenoid which is wound around a section of the permeable core. The permeable core has a gap within which a flux concentrating cold crucible is provided. Melt levitation processing takes place within the cold crucible. A fluid redirection skirt having an intake port partially surrounds the gap and conducts fluid through an exhaust nozzle.

This is a Division of application Ser. No. 08/443,658 filed May 18, 1995now U.S. Pat. No. 5,675,306.

The present invention relates generally to electromagnetic amplificationsystems and, more particularly, to a method and apparatus for thepropulsion of objects using electromagnetic fields.

BACKGROUND OF THE INVENTION

The movement of objects through the influence of electromagnetic fieldsis a widespread engineering practice is with many advantages overmechanical alternatives. One application of this practice is theelectromagnetic levitation of metals for crucibleless processing. Inthis application a body of metal is suspended in space by the inducededdy current repulsion between the metal and a suitably shapedalternating magnetic field. Melting is induced by making the eddycurrents intense enough or through the application of an additional RFfield. The molten metal is then processed and separated while it issuspended in space, thus never coming in contact with a crucible. Verypure, uncontaminated metal products are obtained this way.

A specific electromagnetic levitation melt system designed to combinethe melting, melt treatment, and pouring procedures into a singleoperation was developed at the University of Alabama and described inLevitation-Melting Method Intrigues Investment Casters (March 1991)Advanced Materials and Processes, 42-45. As shown schematically in FIG.1 a metal 101, which is to be processed, initially rests on top of abase plate 102 which has a hole 103 in its center, the hole's diameterbeing slightly smaller than that of the metal billet. When power issupplied to a set of induction coils 104, a current is inducted in metal101 causing it to begin to heat up and gradually melt, melting from topto bottom. The electromagnetic force field created by the interaction ofthe induced current and its associated magnetic field has a rotationalcomponent which stirs the melt. The irrotational component of the fieldpushes against the outside surface of the melt. When the center of thebottom of the billet melts, the liquid metal drops through hole 103 intoa mold 105.

A second type of related application is electromagnetic pumping, where aconducting fluid is propelled along a channel through the interaction ofinduced currents and static or alternating magnetic fields. An overviewof such propulsion systems is given by D. L. Mitchell et al. in anarticle entitled Induction-Drive Magnetohydrodynamic (MHD) Propulsion inJournal of Superconductivity, 6 (4) (1993) 227-235. The authors describethe early research in applying MHD propulsion systems to seagoingvessels during the 1960's through the current research using high fieldsuperconducting magnet technology. A cited example of recent research inthis area is the Yamato I, a 280-ton test vessel utilizing two MHDthrusters incorporating Ni:Ti superconducting magnets cooled byliquid-helium cryostats. The electrical conversion efficiency for theYamato I thrusters is only a few percent. The authors state thatincreasing the efficiency would require, either singly or incombination, an increase in the magnetic field strength, the size of thepropulsion units, or the conductivity of the seawater. The authors alsodiscuss the use of electromagnetic propulsion systems for pumpinghazardous materials and for controlling the liquid sodium flow inbreeder reactors.

A third type of application is known as Maglev. Entire transportvehicles (e.g., trains) can be suspended over guiding rails to yield anearly frictionless high speed mode of transport. A fourth class ofapplications involve the sudden exchange of energy from anelectromagnetic form to a kinetic form or vice versa. The former is thefoundation of rail-gun kinetic energy weapons. The latter is thepreferred approach for the production of MegaGauss fields in smallregions through explosive flux compression.

The most general force law at work in the above applications is theLorentz force between a current and a magnetic field: F=∫×dl. Theefficiency of such a force for accomplishing the propulsion of matter isthen in general proportional to the square of the magnetic field. Thisis clear when the current I is induced by the magnetic field B itself.Since the power wasted is proportional to the Joule heating of theconducting material, even when the current is supplied by a separatesource it is more advantageous to have a high B-field, low currentsystem than a low B-field, high current system. Then for a constantforce F, since the power lost goes as I² R=[F/(Bl)]² R, the advantagealso goes as the square of the magnetic field. For this reason it isdesirable to generate the strongest magnetic fields possible.

At present, the most efficient magnetic field generation systems utilizesuperconductors capable of sustaining thousands of Amperes withnegligible loss. Their main disadvantages are the requirement forcryogenic cooling and the eventual limitation that high field strengthsplace on the superconducting state. The alternative of usingconventional conductors is viewed as impractical because the highcurrents required to produce a strong magnetic field in a given regionof space would eventually melt the conductors.

From the foregoing, it is apparent that a method by which the magneticfield produced by an electric current can be multiplied in amplitude tothe desired strength so that high field strengths can be produced bycurrent carrying conductors with minimized joule heating of theconductors is desired.

SUMMARY OF THE INVENTION

The present invention applies the well known principle of voltageamplification in electric LRC circuits to magnetic L_(m) R_(m) C_(m)circuits, thereby providing an apparatus and a method for theamplification of magnetic fields. One advantage of the present inventionis that it reduces the current loads on the metallic conductors withinan electromagnetic system, assuming that the requirements on themagnetic field strength are kept constant. This advantage is due to theJoule heating load being transferred from the conventional wires to theceramic ferrites that effect the field amplification.

In brief, a resonant magnetic field amplifier according to oneembodiment of the invention consists of an alternating voltage sourcesupplying voltage across the terminals of a solenoid wound around anon-conducting permeable core, the core containing a gap. A section ofthe permeable core is wound around a section of a dielectric core, thedielectric core having a very high, real permittivity. The amplificationfactor of this embodiment is equivalent to the ratio of ωL_(m) to R_(m),where ω is the angular frequency, and L_(m) and R_(m) are the totalmagnetic inductance and the total magnetic resistance of theelectromagnetic system, respectively. To obtain the maximum benefit ofthe amplification factor, the gap must be designed according to theinvention. An improved melt levitation system is provided utilizing themagnetic field amplification within the gap.

In a second embodiment of the invention, a solenoid is wound around aportion of a non-conducting permeable core. An alternating voltagesource is connected to the solenoid. A portion of the permeable core iswound a first number of turns around a section of a dielectric core, thedielectric core having a very high, real permittivity. A secondnon-conducting permeable core is wound a second number of turns around asecond section of the dielectric core. The second permeable corecontains a gap. The amplification factor of this embodiment is definedby the ratio of the second number of turns to the first number of turns.An improved melt levitation system is provided utilizing the magneticfield amplification within the gap. In a separate embodiment of theinvention, the system described above is used to match the magneticimpedance of a transmission line to that of a voltage source.

A further understanding of the nature and advantages of the presentinvention may be realized by reference to the remaining portions of thespecification and the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a prior art electromagneticlevitation melt system;

FIG. 2 is an illustration of a simple magnetic circuit according to theprior art;

FIG. 3 is an illustration of a magnetic circuit in which a section ofthe magnetic core has been wrapped around a dielectric core of veryhigh, real permittivity;

FIG. 4 is an illustration of a magnetic step-up transformer;

FIG. 5 is a graph of the apparent permeability versus the angularfrequency for a specific system of conductors;

FIG. 6 is an illustration of a magnetic step-up transformer configuredto function as a fluid pump;

FIG. 7 is an illustration of a quarter wave resonant amplifier;

FIG. 8 is the structure illustrated in FIG. 7 with a small mmfintroduced near the shorted end;

FIG. 9 is an illustration of a quarter wave resonant amplifierconfigured to function as a simple levitator;

FIG. 10 is an illustration of the termination of the gap ends for a meltlevitation system;

FIG. 11 is an illustration of the flux lines for the gap shown in FIG.10;

FIG. 12 is an illustration of a flux concentrator;

FIG. 13 is an illustration of the eddies induced in the fluxconcentrator of FIG. 12 due to the magnetic flux in the gap;

FIG. 14 is a cross-sectional view of the gap and concentrator shown inFIGS. 10-13 with a metal sample to be levitated in place;

FIG. 15 is an illustration of the gaps in the primary winding of themagnetic step-up transformer shown in FIG. 4 when it is operated as aresonant transformer;

FIG. 16 is an illustration of a magnetic transmission line;

FIG. 17 is an illustration of the fundamental mode field of thestructure shown in FIG. 16;

FIG. 18 is an illustration of a feeding arrangement for the transmissionline of FIG. 16;

FIG. 19 is an illustration of a step-up transformer with a turns ratioof three;

FIG. 20 is an illustration of a quarter wave resonator for seawaterpumping and propulsion;

FIG. 21 is an illustration of a feed mechanism for the resonator shownin FIG. 20; and

FIG. 22 is an illustration of a conventional electromagnetic thruster.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The concept of magnetic circuits is used with advantage in the design ofmagnets and electromagnetic machinery. In such applications it is commonto draw an analogy between a DC electric circuit and an arrangement ofpermeable materials in the presence of a magnetic field source (e.g., asolenoid). This analogy draws an equivalency between the DC voltagesource which provides an electromotive force, emf, and the magnetomotiveforce of the solenoid winding. Thus, in the same way as the voltagesource drops voltage across series resistances in its path, themagnetomotive force is dropped across the series reluctances in itspath. Therefore reluctance is given by the expression R=l/(μA), where μis the permeability of the material carrying the magnetic flux, l is itslength, and A is its cross-sectional area. Clearly an air gap (i.e.,μ=μ₀) in series with a highly permeable core (i.e., μ>>μ₀) has asignificant effect on the overall reluctance of the circuit.

The traditional analogy between reluctance and resistance has been foundto be inappropriate since it only works when the circuit is viewed inthe limit as frequency goes to zero. To obtain the proper analogy thefull duality between dielectric materials and magnetic materials must beinvoked. This was originally effected in 1892 by Oliver Heaviside,Electric Papers, chap. XXX, sec. III, 441 (2nd ed. 1970). Heavisideconceived of a quantity analogous to electric current which he termedmagnetic current. He defined the magnetic current asG=fH+[μ/(4π)][∂H/∂t]. The second term on the right hand side of theequation is the conventional rate of change of the magnetic induction.Heaviside introduced the first term: the magnetic conduction currentwhich can only exist if magnetic conductivity f exists.

Although magnetic conductivity has never been observed to exist at zerofrequency (i.e., DC), it is clear that in the presence of alternatingcurrents it can exist. In particular, by letting the magnetic field beharmonic with a time dependence e^(j)ωt, and identifying μ=μ' andωμ"=4πf, then the magnetic current equation can be rearranged into:

    4πG=ωμ"H+jωμ'H=jωH(μ'-jμ")

It is also clear that a material with a complex permeability containinga lossy or imaginary part, μ", behaves as if it were carrying a magneticconduction current.

Although Heaviside assumed the magnetic conductivity to be small, thepresent derivation assumes that it is very large. It is assumed that themagnetic conductivity is large enough to overwhelm the properties of thematerial in the same way that a metal's conductivity overwhelms itsdielectric properties. It is then straightforward to show that such amaterial, driven by a harmonic magnetomotive force, can be made todisplay many characteristics analogous to those found in AC electriccircuit elements. Therefore just as the electricinductance-capacitance-resistance (LRC) circuit is the foundation of avast array of practical applications, a new magnetic inductance-magneticcapacitance-magnetic resistance (L_(m) R_(m) C_(m)) circuit is proposedas the foundation for the present invention.

I. Dual Circuit Parameters

The prior art magnetic circuit of FIG. 2 consists of an alternatingvoltage source 1 supplying voltage V connected across the terminals of asolenoid 2 of height h₁ with N₁ turns carrying the current I₁. Solenoid2 is wound on a non-conducting permeable core 3 of complex permeabilityμ, where μ is equivalent to μ'-jμ", and where μ' is the real part of thecomplex magnetic permeability and μ" is the imaginary part. Permeablecore 3 has a total length l, a cross-section radius ρ and its two endsare parallel to each other but separated by a gap 4 of length g.

Solenoid 2 provides a magnetomotive force mmf₁ =I₁ N₁ which must equalthe circuital line integral of the magnetic field throughout the wholeflux path. Assuming no leakage into the surrounding space, the fluxflowing through core 3 must traverse gap 4 unchanged. Therefore, if forsimplicity we assume that the end faces of core 3 and gap 4 have thesame radius as the cross-sectional radius of the core, the B-field incore 3 and gap 4 are equal (as would be demanded by the electromagneticboundary condition on the normal B-field). Then

    mmf.sub.1 =I.sub.1 N.sub.1 =∫o·=(B/μ)l+(B/μ.sub.0)g(1)

Multiplying the numerator and denominator of each term on the right handside by the angular frequency ω and the complex number j=(-1)^(1/2) andseparating the core permeability into real and imaginary parts, equation1 becomes:

    mmf.sub.1 =[(jωμ'Hl+ωμ"Hl)/(jωμ'+ωμ")]+[(j.omega.μ'Hg+ωμ"Hg)/(jωμ.sub.0)]             (2)

Now select the magnetic permeable material to have a natural or inducedspin resonance at or just below the operating frequency, thus allowingμ" to be much greater than μ'. Such materials exist in nature, with spinresonances conveniently ranging from the kHz (e.g., manganese zincferrites) into the MHz range (e.g., nickel zinc ferrites). A magneticconductivity σ_(m) =ωμ" is defined such that a magnetic conductioncurrent density J_(m) can be defined as J_(m) =σ_(m) H. Then equation 2simplifies to:

    mmf.sub.1 =[(J.sub.m l)/σ.sub.m ]+[(J.sub.m g)/(jωμ.sub.0)](3)

Multiplying the numerators and denominators by the cross-sectional areaof core 3 (i.e., πρ²), rearranging terms and identifying the totalmagnetic current as I_(m) =J_(m) πρ², yields:

    mmf.sub.1 =I.sub.m /G.sub.m +I.sub.m /(jωC.sub.m)    (4)

where G_(m) is the total dual magnetic conductance which is thereciprocal of the total dual magnetic resistance,

    G.sub.m =(σ.sub.m πρ.sup.2)/l=1/R.sub.m       (5)

and C_(m) is the dual magnetic capacitance of the gap,

    C.sub.m =(μ.sub.0 πρ.sup.2)/g                    (6)

For these circuit elements to be useful they must be designable. Avariety of values must be obtainable by geometry and material choice toallow a required circuit operation to take place in a given application.Clearly, the core material and geometry can be used to obtain a varietyof magnetic resistances. Magnetic materials exist ranging from verylossy to virtually lossless. However, it is not clear from the abovethat given a choice for the magnetic resistance, the magneticcapacitance is truly designable.

This doubt arises because if the gap is as described, submerged in air,the capacitance term has a minimum limit. That is, when the two faces ofthe gap are allowed to become arbitrarily separated, we can only lowerthe total capacitance to the series sum of the self capacitance of eachface to infinity, which is of the order of πμ₀ ρ. Trying to depress thecapacitance below this limit by narrowing down the gap faces (reducingthe cross-sectional area locally) will not work because the flux willstill leak out over a larger area. However, by taking advantage of theeddy currents induced in conductors by the alternating magnetic field inthe gap, it is possible to depress the magnetic capacitance below thisvalue. For example, if a metal sheet with a hole smaller than thecross-sectional area of the core is inserted into the gap, the magneticflux will be forced to flow through this smaller area by the eddycurrents induced in the sheet. This effect is exploited in the presentinvention, for example by immersing the gap in a conducting fluid. Usingthis technique, small magnetic capacitances can be obtained. Largecapacitances are not difficult to achieve since the gap can be madearbitrarily small.

All that is missing from the desired L_(m) R_(m) C_(m) circuit is themagnetic inductance. This is derived as follows.

The changing magnetic flux inside core 3 will induce a circulatingelectric field inside the core and in the surrounding space. ByMaxwell's equations, this field is driven by a circuital electromotiveforce (emf) so that:

    emf=∫o.sub.induced ·dl=-jω∫·(7)

Since all quantities are harmonic in time, the changing electric fieldthen constitutes a changing electric displacement flux so that there isan induced back mmf due to:

    mmf=∫o·=jω∫·=jω∫ε.sub.induced ·                                         (8)

This back mmf has an internal component due to the displacement fluxcrossing the inside of core 3 (which can have a substantial dielectricconstant ranging from 10 to 10⁴) and an external component from thetotal flux in the surrounding space. Assuming that the frequency ofoperation is to be in the MHz range, the core choice would be a nickelzinc type of ferrite with a natural spin resonance in the MHz range anda dielectric relaxation in the kHz range. In this case, the relativepermittivity of core 3 would be of the order of 10, minimizing theinternal contribution. Whatever the choice of the materials it is clearthat this back mmf of equation 8 is entirely equivalent to the back emfthat wires experience in the presence of alternating currents due toself inductance. In other words, a core of high imaginary permeability,carrying an alternating magnetic current, also sees a magneticinductance.

To maximize this term, consider the configuration of FIG. 3 where asection of a magnetic core 10 has been wrapped around a dielectric core11 of very high, real permittivity. In effect, magnetic core 10 becomesa dual solenoid of n₁ turns, internal radius r₁ and length h_(m).

The electric field inside the solenoid is given by the totalelectromotive force n₁ I_(m) dropped across the length l_(m) ofdielectric core 11:

    E=(n.sub.1 I.sub.m)/l.sub.m                                (9)

The alternating displacement vector is then:

    D=(εn.sub.1 I.sub.m)/l.sub.m                       (10)

Leading to a total back mmf accumulated over the n₁ turns of:

    mmf.sub.ind =n.sub.1 ·jω[(εn.sub.1 I.sub.m)/l.sub.m ]πr.sub.1.sup.2                                        (11)

where we identify the magnetic inductance as L_(m) =(εn₁ ² πr₁ ²)/l_(m).The value of this inductance is clearly controlled by the material andgeometry chosen for the dielectric core. Therefore, the magnetic circuitof FIG. 3 is the desired L_(m) R_(m) C_(m) circuit and it is resonant,per the equation:

    mmf=I.sub.m R.sub.m -[j/(ωC.sub.m)]I.sub.m +jωL.sub.m I.sub.m(12)

where all inductive terms, including the self, are lumped into theL_(m). Solving for the total magnetic current:

    I.sub.m =(I.sub.1 N.sub.1)/[R.sub.m -j/(ωC.sub.m)+jωL.sub.m ](13)

The effect of this magnetic current on the driving voltage source can bededuced as follows. Assume that the voltage source-solenoid combinationhas negligible circuit capacitance, then the voltage supplied by source1 must be dropped across the ohmic resistance of the solenoid wire andthe opposing back emf of the solenoid's inductance. The latter is aresult of equation 7. For N₁ turns of wire the total induced voltage is:

    V.sub.ind =N.sub.1 {-jωBπρ.sup.2 }=N.sub.1 {-jω(μ'-jμ")Hπρ.sup.2 }≅N.sub.1 {-ωμ"Hπρ.sup.2 }

so that:

    V.sub.ind =-N.sub.1 I.sub.m                                (14)

Together, equations 13 and 14 give the relationship between the magneticdual circuit elements and the source voltage:

    V.sub.1 =I.sub.1 {R.sub.wire +[N.sub.1.sup.2 /(R.sub.m -j/(ωC.sub.m)+jωL.sub.m)]}                    (15)

II. Methods for the Amplification of Magnetic Fields

1. The Resonant Amplifier

The magnetic L_(m) R_(m) C_(m) circuit defined by equation 13 can beutilized as a resonant magnetomotance amplifier analogous to resonantelectric LRC circuits. In conventional LRC circuits it is known that ifthe inductive term and the capacitive term are made equal to each other,the electric current in the circuit is only limited by the smallresistance of the wire. The flow of this large current through thereactances of the inductor and capacitor can develop a large voltage.The requirement for voltage amplification is that the reactances of theinductor and capacitor be greater than the resistance of the wire (inother words, that the Q of the circuit be large). The same principleapplies in the case of the dual magnetic resonant circuit.

As an example of a dual magnetic resonant circuit, consider thearrangement of FIG. 3 where l, the total length of core 10, is λ/71, andwhere λ=2πc/ω. Let l be as small as possible, on the order of l≅3h_(m)+n₁ 2πr₁. Let r₁, the internal radius of the dual solenoid, equal 10ρ.

If h_(m) =n₁ 2ρ, then by winding both sides of magnetic core 10 arounddielectric core 11, l_(m) can be made to be less than or equal to2h_(m).

And we have l=69n₁ ρ, which implies that ρ=λ/4899n₁.

Now, the ratio between ωL_(m) and R_(m) is ##EQU1##

With l=λ/71 the magnetic Q_(m) becomes:

    Q.sub.m =5.93×10.sup.-6 [(μ.sub.r "ε.sub.r)/n.sub.1.sup.2 ](17)

Finally, if we assume for simplicity only one turn of the dual solenoid(i.e., n₁ =1) and if the relative permeability of core 10 is of theorder of 5000 and the relative permittivity of dielectric core 11 isalso the same (e.g., barium titanate ceramics), then Q_(m) =147. Inother words:

    ωL.sub.m =147R.sub.m which at resonance must also equal 1/(ωC.sub.m).                                       (18)

The condition for resonance is then:

    g/(ωμ.sub.0 πρ.sup.2)=147[l/(ωμ.sub.r "μ.sub.0 πρ.sup.2)]                                         (19)

So that,

    g≅0.02941≅2ρ                       (20)

Therefore a magnetic circuit with the design parameters given above willresonate when gap 4 is of the order of the diameter of magnetic core 10,with a Q_(m) of 147. Q_(m) is the magnetic field amplification factor.This is proven as follows.

By the continuity of normal B, neglecting fringing, the flux insidemagnetic core 10 must continue inside gap 4. That is:

    -jμ"H.sub.core πρ.sup.2 =μ.sub.0 H.sub.gap πρ.sup.2 or H.sub.gap =-jμ.sub.r "H.sub.core                       (21)

Since at resonance the whole magnetomotive force drops across the R_(m)term,

    H.sub.core =(I.sub.1 N.sub.1)/l=(I.sub.1 N.sub.1)/33.7g    (22)

And equation 21 becomes

    H.sub.gap =-j147[(I.sub.1 N.sub.1)/g]                      (23)

If instead of this resonant magnetically conducting core a conventionalcore of real permeability and with no resonance had been used in theconfiguration suggested in FIG. 2, it is well known that all the mmfsupplied by the current would be dropped across the gap. Thus, inconventional arrangements the magnetic field produced by the current I₁in a gap of size g is:

    H.sub.conventional =(I.sub.1 N.sub.1)/g                    (24)

Therefore, an amplification of a factor of Q_(m) has been accomplishedby the disclosed invention. The current through the wire solenoid hasnot been increased. The increased magnetic field power density comesfrom an increased electric field power density at the supplying voltagesource since the voltage is higher than that required to flow I₁ throughthe wire resistance, according to equation 15.

Clearly, larger values of permeability, permittivity and the totallength of the magnetic circuit relative to the free space wavelength allincrease the Q_(m) amplification factor proportionately. However, toinsure resonance as Q_(m) is increased, the magnetic capacitance must bemade correspondingly smaller. In electric circuits there is a limit tothis process since as two capacitor plates are separated, the circuitcapacitance does not go to zero but tends to the limit of one half ofthe self capacitance between each plate and infinity. In the magneticcircuits of the present invention, however, it is possible to go belowthis limit by using conducting fluids.

2. Magnetomotance Step-Up Transformer

The second example of the amplification of magnetic fields parallels theamplification of voltages in step-up transformers. Consider the magneticcircuit of FIG. 4. Voltage source 1 is driving an electric current I₁through the solenoid which constitutes a magnetomotive force mmf₁ =I₁ N₁driving a magnetic current I_(m1) in a first magnetically conductingcore 15. Core 15 is assumed to form a closed circuit and to be wound inn₁ turns around a dielectric toroid 16 of cross-sectional radius r₁ andpermittivity ε. It is assumed that in first core 15 the ωL_(m) term isgreater than its R_(m) term and dominates the behavior. A secondmagnetically conducting core 17 is wound n₂ turns around toroid 16 andleft open at a gap 4 of size g.

It has already been shown by equation 10 that the dielectricdisplacement inside toroid 16 due to the flowing I_(m1) is D=(εn₁I_(m1))/l_(m). This displacement vector alternating through the toroid'scross-sectional area inside the dual solenoid made by second magneticcore 17 induces, by equation 11, a magnetomotive force of mmf₂ =n₂·jω[(εn₁ I_(m1))/l_(m) ]πr₁ ² on the second solenoid. If the capacitiveterm of the gap in the second core can be made to dominate the behavior,then all this mmf₂ will be dropped across gap 4. Recognizing that forthe first core being dominated by ωL_(m) means that mmf₁ =n₁ ·jω[(εn₁I_(m1))/l_(m) ]πr₁ ² : ##EQU2##

Again, the magnetic field inside the gap has been made greater thancould be accomplished with the same current in a conventionalarrangement. This time the amplification factor is the turns ratio n₂/n₁.

The success of this step-up scheme for amplification lies in the abilityto make the dual reactance of the magnetic capacitance componentdominate the circuit of the second permeable core. To accomplish this,the term C_(m) must be made as small as possible. As previouslydiscussed, in a free space environment this is impossible because thelower limit of C_(m) is of the order of πμ₀ ρ. To prove this, note thatthe capacitive reactance is of the order 1/(ωπμ₀ ρ) whereas theinductive is ωL_(m) =(ωεn₂ ² πr₁ ²)l_(m). Letting l_(m) =2h_(m2) =4ρn₂and r₁ =10ρ as before and defining P as the ratio of the capacitivereactance to the inductive, then:

    1/(ωC.sub.m)=PωL.sub.m or P=[1/(ωπμ.sub.0 ρ)][l.sub.m /(ωεn.sub.2.sup.2 πr.sub.1.sup.2)]=(4ρn.sub.2)/(ω.sup.2 μ.sub.0 ε.sub.0 ε.sub.r n.sub.2.sup.2 π.sup.2 100ρ.sup.3)(26)

which, using the design parameters from section II[1] described above,reduces to:

    P.sub.freespace =0.98/n.sub.2                              (27)

Since n₂ is greater than 1, it is clear that in free space we cannotmeet the requirement of P>1, and the capacitive term will not dominate.However, if the gap is immersed inside a conducting fluid the magneticflux in the gap will induce an electromotive force that will drivevolumetric eddy currents in the fluid.

In such an arrangement the driving emf on the order of I_(m) worksagainst an impedance equal to the sum of the resistance through thefluid plus the self-inductance of the circulating current. Defining theself-inductance of the circulating current as L_(eddy), then:

    I.sub.eddy ≅I.sub.m /(R.sub.eddy +jωL.sub.eddy)(28)

And this I_(eddy) constitutes the back mmf on the magnetic circuit. Ifthe fluid conductivity is high enough, the current is inductance limitedand I_(eddy) ≅I_(m) /(jωL_(eddy)). Adding this term to the other backmmf's in equation 12 gives:

    mmf=I.sub.m R.sub.m -[j/(ωC.sub.m)]I.sub.m +jωL.sub.m I.sub.m -[j/(ωL.sub.eddy)]I.sub.m                           (29)

From equation 29 it is clear that the eddy current term in theconducting fluid is in phase with, and therefore increases, the magneticcapacitive reactance. In fact, we can combine the two terms into one anddefine the magnetic capacitive reactance 1/(ωC_(m)) to be of the orderof 1/(ωμ(ω)ρ). Here μ(ω) is the effective permeability of the conductingmedium as a function of frequency.

For a system of conductors (such as laminated magnetic metal cores) ofcharacteristic dimension t, μ(ω) has the behavior shown in FIG. 5. FIG.5 illustrates that when the frequency is such that the characteristicdimension is of the order of two skin depths, the real permeability hasdropped to half the free space value and an imaginary component arisesof approximately the same magnitude. This frequency is called the eddyfrequency, f_(e), which is equal to ω_(e) /(2π). As the frequencyincreases both μ' and μ" drop as 1/ω^(1/2). Therefore, if the frequencyis significantly greater than the eddy frequency, μ(ω)≈μ₀ (ω_(e)/ω)^(1/2).

If the conducting fluid is sea water (i.e., conductivity approximately 5mhos/meter) and the characteristic dimension g is equal to 2 meters,this eddy frequency is 0.04 MHz. If the circuit operates at 50 MHz thenμ(ω) is equal to 0.028 μ₀, which increases the magnetic capacitivereactance by a factor of 35. This makes the ratio P of the capacitivereactance to the inductive reactance of equations 26 and 27 of the orderof 3.5 for a secondary core of n₂ =10 turns. In this instance 78% of themmf₂ is dropped across the gap or 7.8 mmf₁. If n₂ =20 turns, the ratio Pis 1.75 and 64% of the mmf₂ is dropped across the gap or 12.7 mmf₁.Therefore it is straightforward to obtain an amplification of one orderof magnitude using the step-up principle in sea water.

3. Step-Up Transformer Pump

As discussed above, if the gap in the step-up transformer configurationis immersed in a conducting fluid, strong eddy currents are induced inthe fluid. Due to the reaction of the currents in the fluid to theamplified magnetic field, the fluid in the gap is expelled radiallyoutwards from the gap. This outward force can be used in a variety ofapplications.

The simplest application of the outward force on the fluid within thegap is to use the step-up transformer configuration as a magnetic fluidstirrer. For this application the step-up transformer does not have tobe modified, the gap is simply immersed in the fluid to be stirred.

A more useful application is to channel the force exerted on the fluidwithin the gap, thereby creating a fluid pump. One method of channelingthe fluid flow is shown in FIG. 6. Surrounding gap 4 is a fluidredirection skirt 5 containing both a plurality of fluid intake ports 6and a fluid exhaust nozzle 7. Skirt 5 is made of a material which isessentially transparent to the electromagnetic waves; plastic in thepreferred embodiment. As the fluid is expelled outwards from the gap,the skirt redirects the outward flow through exhaust nozzle 7,generating a propulsive force.

4. Resonant Magnetic Step-Up Transformer

This method is a combination of the resonant amplifier and themagnetomotance step-up transformer described above. In this case boththe primary and secondary cores are tuned to resonance through thesuitable arrangement of all dual capacitances and inductances. Thestepped up mmf then gets multiplied by the resonance amplification toobtain a total magnetic field amplification in the gap that is as aminimum, the product of the two amplifications disclosed in thepreceding two sections (greater than 2 orders of magnitude) and as amaximum could be a quantity comparable to the voltage amplificationobtained in a Tesla coil (six orders of magnitude) provided magneticmaterials with extremely high magnetic conductivity are used.

5. Quarter Wave Resonant Amplifier

FIG. 7 is an example of a quarter wave resonant amplifier. It consistsof a dual coaxial transmission line constructed from a lossy permeablematerial, shorted at end 20 by the same material. End 21 is left openand sealed against surrounding external conducting fluid by a plasticbarrier 22. Since a conducting fluid has been shown to enhance themagnetic capacitive reactance term, the open end 21 of the dualtransmission line so constructed can truly approach the ideal definitionof a magnetic open circuit. When a small mmf is introduced into thisstructure near shorted end 20, as suggested by the connection scheme ofFIG. 8, a standing wave will be set up inside with a minimum of magneticfield strength at shorted end 20 and a maximum at open end 21 in thefluid. This constitutes a dual quarter wave resonant line section.

To derive the equations of the dual coaxial line assume the line isfilled with a low loss dielectric 23. Because the walls of the coaxialwaveguide are made of a lossy magnetic material, the tangential magneticfield tends to vanish on their surface. As a result, the structuresupports a TEM mode in which the magnetic field is purely radial (normalto the coaxial surfaces) and the electric field circulates tangential tothe same. The magnetic skin depth inside the lossy magnetic material is:

    δ.sub.m =[2/(ωεσ.sub.m)].sup.1/2 (30)

The magnetic impedance (which has the units of a conventionaladmittance) of the transmission line is then: ##EQU3## where the R_(m),L_(m) and C_(m) are per unit length.

For a resonant quarter wave section of line a small "voltage" input 1near shorted end 20 appears greatly amplified at open end 21 by thefactor:

    Q.sub.m =(2ζ)/[R.sub.m (λ/4)]                  (32)

If the thickness of the magnetic conductors is greater than the magneticskin depth, the magnetic resistance per unit length is just: ##EQU4##

In a typical embodiment filling dielectric 23 would be a ceramic of highdielectric strength in order to withstand the amplified electric fieldinside the transmission line and its relative permittivity would bechosen to be 200. With this dielectric and a frequency of operation of25 MHz, the quarter wave length, l, is 0.21 meters. If the imaginarypart of the relative permeability of the magnetic conductor is 5000(either natural or enhanced through ferromagnetic resonance in thepresence of an applied DC magnetic field) and the real part of itspermittivity is on the order of 10, then the magnetic skin depth, δ_(m),is 0.012 meters. For an inner coax cylinder's outer radius, a, of 0.0381meters and an outer coaxial shield's inner radius, b, of 0.105 meters,then the magnetic resistance per unit length is 0.000478 mhos/meter,while the transmission line magnetic impedance is 0.00606 mhos, yieldingan amplification factor of Q_(m) =120.8.

6. Quarter Wave Resonator Levitation System

The quarter wave resonant amplifier can be reconfigured to act as asimple levitator. In this configuration the resonator of FIG. 7 does notcontain barrier 22. Instead of immersing the device in a conductingfluid, an electrically conducting ground plane 25 is placed at end 21 asshown in FIG. 9. In this configuration, the resonator would floatapproximately a quarter wave above the ground plane. Even though thereis a gap, the energy in the resonator tends to be trapped inside thedevice. It cannot leak out because the electric field inside the deviceis circular and tangential to the ground plane. Such a wave cannotpropagate over the ground.

7. Magnetic Material Requirements

Regardless of the configuration of the magnetic amplifier, the magneticmaterials employed in the amplifier must be sufficiently lossy. It isimperative that the imaginary part of the complex permeability be muchgreater than 1 at the magnetic amplifier's frequency of operation sothat the lossy permeable core will behave as the magnetic equivalent ofa metallic conductor. Generally this requires that if the frequency ofoperation is to be in the MHz range, μ" is of the order of 1000 to 5000times μ₀. For other frequencies of operation, the product of theimaginary permeability and the frequency must be kept approximatelyconstant. Therefore, if the frequency of operation is to be in the kHzrange, μ" is of the order of 10⁶ to 5×10⁶ times μ₀ while if thefrequency of operation is to be in the GHz range, μ" is of the order of1 to 5 times μ₀.

The characteristics of magnetic materials are well known and thereforeit is simply a matter of selecting an appropriate material for aspecific application, appropriateness being based on the material'spermeability for the intended frequency of operation, its mechanicalcharacteristics, its availability in the desired sizes, its ability towithstand the intended environment, and its cost.

In general, the peak imaginary permeability is of the order of one halfto one times the initial permeability. Therefore, manganese zinc ferriteclasses III and IV with initial permeabilities on the order of 3000 to20,000 and 2000 to 5000, respectively, as well as class VI nickel zincferrites with an initial permeability of 1000, are excellent candidatesfor a variety of magnetic amplifier applications. In the GHz range,cobalt zinc ferrites have suitable properties. It is also possible toachieve a fully controlled high lossy permeability by applying anexternal DC magnetic field to the magnetic core, this technique ofcontrolling a material's permeability being well known in the art.

III. Specific Examples

1. Resonant Magnetic Circuit Melt Levitation System

In this example an electromagnetic melt levitation system operating at100 kHz is described according to the present invention. The levitationforce is produced by the interaction between the flux and the eddiesinduced in the metal sample.

This embodiment utilizes the basic design structure illustrated in FIG.3. In this embodiment dielectric core 11 is a toroid made of Crowloy 70.It has a rectangular cross section 0.94 meters wide by 0.3 meters thickand it offers a circular path to the displacement vector of mean radius0.35 meters. At 100 kHz: ε'/ε₀ =123,000; tgδ_(d) =0.64×10⁻⁴ ; μ'/μ₀=400; and tgδ_(m) ≈0. Magnetic winding 10 is made of manganese zincferrite according to the composition disclosed by E. Roess in MagneticProperties and Microstructure of High Permeability MnZn Ferrites,Ferrites: Proceedings of the International Conference, July 1970, Japan,203-209. The radius of the magnetic winding, ρ, is 0.01 meters and has atotal length of 419 meters. At 100 kHz: μ"≧10⁴ μ₀. Magnetic winding 10is wound around the dielectric core in three layers of windings for atotal of 159 turns (n₁). Source 1 is 4 turns of 000 gauge copper wirewound around a section of magnetic winding 10.

The total magnetic resistance per equation 5 is: ##EQU5##

The magnetic inductance per equation 11 is εn₁ ² A/l_(m) where A is thecross-sectional area of dielectric core 11 and l_(m) is its mean length.In this case A=0.3×0.94=0.282 m² and l_(m) ≈2π(0.35)=2.2 m. Thereforethe magnetic inductive reactance term is: ##EQU6## Therefore themultiplication factor for the magnetic field is:

    Q.sub.m =2217/169=13.

To use this system as a melt levitation system the ends of the gap areterminated as shown in FIG. 10. The flux lines for this gap are shown inFIG. 11. The mean magnetic flux path is on the order of 0.02 meters. Inair, the magnetic capacitance of the gap is approximately μ₀ π(0.01)²/0.02 and the magnetic capacitive reactance is 1/ωC_(m) or 80.6 mhos.

To guarantee resonance, a water cooled cold crucible is designed whichalso acts as a flux concentrator as shown in FIG. 12. The concentratorshapes the field within the gap and drops C_(m). The magnetic flux inthe gap induces eddies in the flux concentrator as shown in FIG. 13. Theeddies induced on the back wrap around to the front, effectively forcingthe magnetic flux to flow through the gaps 30 in the concentrator andfan out within the interior.

FIG. 14 is a cross-sectional view of the gap and concentrator with ametal sample 31 to be levitated in place. If the combination of thecrucible gap flux compression and the eddies induced in the levitatedmetal reduce the magnetic flux path cross-section by a factor of 27.5,C_(m) is dropped by the same factor and 1/(ωC_(m)) increases from 80.6mhos to (80.6) (27.5)=2217 mhos. Therefore jωL_(m) =-j/(ωC_(m)) and themagnetic circuit resonates.

To obtain the desired 27.5 factor, concentrator gaps 30 must beapproximately 0.0004 meters. As metal sample 31 melts and flows out ofthe levitation crucible, resonance is maintained by varying thefrequency, ω.

The advantages of the present invention are obvious in light of aconventional melt levitation system. To melt a copper sphere with aradius of 0.01 meters at 100 kHz, a conventional system usesapproximately 800 A. Assuming a four turn configuration, the approximatelevitating field is 160,000 A/m. The magnetic pressure that such a fieldcan exert is (μ₀ /2)H² ≅1.6×10⁴ N/m². A metal sphere of radius 0.01meters has a cross-sectional area of π(0.01)² =3.14×10⁻⁴ m². After theeddy currents are set-up, the effective area influenced by the magneticfield which sees the full pressure is on the order of a tenth of thisarea, or 3.14×10⁻⁵ m². The levitating force is therefore (1.6×10⁴)(3.14×10⁻⁵)=0.5 N. This force is sufficient to levitate 0.05 kg ofmetal, which is approximately the weight of a copper sphere of radius0.01 meters.

Assuming a 10 mm diameter wire with a skin depth of 0.21 mm and aconductivity of 6×10⁷ moh/m, the power wasted on the metal coilscarrying the 800 A is approximately 350 watts (R_(w) [800]² =[5.5×10⁻⁴]800² =350). Note that the power dissipated in the metal to be melted ison the order of tens of kilowatts.

In contrast, by using the above described embodiment of the inventionwith its multiplication factor of approximately 13, only 61.5 A arerequired to achieve the same melt levitation field with the same fourturn configuration (800/13=61.5). In this case the power dissipated bythe metal coils is only 2 watts ([5.5×10⁻⁴ ][61.5]² =2) thus leading tomuch cooler exciting coils. Instead of dissipating the wasted power inthe exciting coil, the melt levitation system using the presentinvention dissipates the power in the ferrite magnetic winding. In thisembodiment:

    R.sub.m =169 mhos

    I.sub.m =mmf/R.sub.m =4(61.5)/169=1.46 volts

The wasted power is then I_(m) ² R_(m) =(1.46)² (169)=360 watts.Therefore approximately the same amount of power is wasted (within thetolerance of the calculations) however in the magnetic resonant circuitthere is very little heating of the exciting coil. Instead the ceramicferrite absorbs the heat.

2. Resonant Magnetic Transformer for Levitation Melt Applications

This embodiment utilizes the basic design illustrated in FIG. 4 and usesthe same materials as described in the previous example. Primary winding15 on which current source 1 is wound is comprised of 47 turns for atotal length of 128 meters. Secondary winding 17 is comprised of 112turns for a total length of 291 meters. The characteristics of theprimary are:

R_(m) =51.6 mhos

ωL_(m) =193.7 mhos

Q_(m) =3.75

The characteristics of the secondary are:

R_(m) =117.3 mhos

ωL_(m) =1100 mhos

Q_(m) =9.38

The turns ratio is 112/47=2.38.

The secondary feeds the same air gap as in the previous levitation meltsystem except in the present embodiment ωL_(m) equals 1100 instead of2217. Therefore the C_(m) only has to be increased by 13.6 instead of27.5. This allows the gap in the flux concentrator to be larger,approximately 0.0008 meters. This configuration yields the 1/(ωC_(m))required to achieve resonance and a multiplication factor Q_(m) of 9.38.

In this configuration the primary must also have a C_(m) low enough toresonate. This can be accomplished by segmenting the winding on everyturn with a gap of 0.001 meters as shown in FIG. 15. In thisconfiguration the total series magnetic capacitance is [μ₀ π(0.01)²]/[47(0.001)], giving a capacitive reactance of 189 ohms. This is on theorder of ωL_(m), thus achieving resonance.

In order to show the performance improvement offered by this embodimentof the invention, assume that the desired magnetic field in the air gapis the same as in the previously described embodiment. Since theconcentrator factor is smaller in this case, I_(m) in the secondary mustbe larger than in the first device. Therefore:

    I.sub.m(secondary) =1.46 (25.7/13.6)=2.75 volts

    mmf.sub.secondary =2.75 volts×117.3 mhos=322.6 amp-turns

    mmf.sub.primary =mmf.sub.secondary /turns ratio=135.5 amp-turns

Since the primary has a Q_(m) of 3.75:

    mmf.sub.source =36 amp-turns

Therefore, for 4 turns the total source current is 9 amps. This is muchless than the 800 amps required by the conventional melt levitationsystem. In order to achieve this low power dissipation in the windings,the ferrite must dissipate a greater amount of power. For thisembodiment:

    Secondary dissipates (2.75) 2(117)=884 watts

    Primary dissipates (135.5).sup.2 /51.6=355 watts

    Winding dissipates (9).sup.2 (5.5×10.sup.-4)=0.04 watts.

3. Step-Up Transformer for Matching Transmission Line to a Source at 25MHz

FIG. 16 is an illustration of a magnetic transmission line. Sides 40 arecopper plates approximately 1 millimeter thick. Sides 41 are high lossferrites in which t.sub.μ is 0.04 meters and μ" is approximately 5000.The cross-sectional dimensions are 0.3 meters by 0.3 meters. FIG. 17illustrates the fundamental mode field of this structure. The structurehas a wave impedance of 377 ohms and a transmission line magneticimpedance, ζ, of 1/377 or 0.0026 mhos.

Assuming that we wish to feed this transmission line with a 50 ohmvoltage source, equation 15 gives an impedance seen at the source of:

    V.sub.source /I.sub.source =R.sub.wire +[(N.sub.1.sup.2)/(R.sub.m +ζ.sub.m)]

Therefore for the feeding arrangement shown in FIG. 18 and assumingR_(m) ≈0, R_(wire) ≈0 and there is only one turn, then there is amismatch since the source sees 377 ohms instead of 50 ohms. To correctthis mismatch we note that in the step-up transformer of FIG. 4:

    mmf.sub.2 =(n.sub.2 /n.sub.1)mmf.sub.1

    I.sub.m2 =(n.sub.1 /n.sub.2)I.sub.m1

and therefore

    ζ.sub.m2 =mmf.sub.2 /I.sub.m2 =(n.sub.2 /n.sub.1).sup.2 (mmf.sub.1 /I.sub.m1)=(n.sub.2 /n.sub.1).sup.2 ζ.sub.m1

The magnetic step-up transformer transforms magnetic impedance throughthe turns ratio. To obtain a match to the 50 ohm voltage source we needto step-up the transmission line impedance from 0.0026 mhos to 0.02 mhosor by a turns ratio of (0.02/0.0026)^(1/2) 32 2.8≈3. Therefore a step-uptransformer with a turns ratio of 3 as shown in FIG. 19 will match thesource with the transmission line.

In the step-up transformer of FIG. 19, a first winding 45 is made of amaterial with μ"≈3000 at 25 MHz, a radius of 0.005 meters and a totallength of 0.6 meters. A second winding 46 is made of the same materialas the first winding and due to its three turns has a total length of1.2 meters. Dielectric core 47 has a radius, r₁, of 0.048 meters, atotal length, l_(m), of 0.444 meters and a ε' of 5000ε₀.

From equation 11 we get: L_(m) =(ε_(r) 'ε₀ n² πr₁ ²)/l_(m) Therefore:##EQU7## The magnetic resistance is: ##EQU8## Since ωL_(m) is greaterthan R_(m) in each case, the circuits are inductance limited and thestep-up transformation occurs.

Thus a transmission line of magnetic impedance 0.0026 mho is transformedby the ratio ωL_(m)(3 turns) /ωL_(m)(1 turn) =9 to 0.0234 mhos and a oneturn loop connected to a 50 ohm source will read an impedance of1/0.0234=43 ohms, effectively matched to 50 ohms.

Therefore what started out as a mismatch of 7.5:1 (i.e., 377/50) hasbecome 1.16:1 (i.e., 50/43) match using this embodiment of theinvention. A closer match can be achieved by careful adjustment of theparameters.

4. Quarter Wave Resonator for Seawater Pumping and Propulsion at 25 MHz

FIG. 20 is an illustration of a quarter wave resonant amplifier. Thisembodiment consists of a magnetic coaxial transmission line 0.25 meterslong in which the outer cylinder 55 has a wall thickness of 0.024meters. Outer cylinder 55 has a shorted end 56. Cylinder 55 and end 56are both made of a lossy permeable material with μ" equal to 5000 μ₀.The inner radius, b, of cylinder 55 is 0.105 meters. The inner coaxcylinder 57 has an outer radius, a, of 0.0381 meters. Plastic barrier 58seals the open end of the transmission line and is approximately 0.002meters thick and mounted 0.21 meters (i.e., λ/4) from shorted end 56.Volume 59 is filled with a dielectric and volume 60 is filled withseawater. In this embodiment the dielectric is a ceramic filled foam,such as barium strontium titanate which has an ε' of 2800, at 7%density. Volume 60 can also be filled with alternating ceramic disks andfoam spacers. For example, 20 ceramic disks each with a thickness of0.000744 meters separated by 20 foam spacers of 0.0097 meters thicknesscan be used.

In order to set-up a standing wave inside the resonator, a small mmf isintroduced into the structure, for example using a one turn coil nearthe seawater end as shown in FIG. 21. In this case the input mmf, isequal to I and the amplified mmf₂ is equal to 120.8 I (the amplificationfactor, Q_(m), of 120.8 was previously derived in Section II[5]).Therefore at the open end:

    H(r)=(120.8I)/r

with a pressure distribution equal to:

    (μ.sub.0 /2)H.sup.2 =(μ.sub.0 /2)(120.8).sup.2 (I.sup.2 /r.sup.2)

Thus the force at the mouth of the waveguide is:

    (μ.sub.0 /2)(120.8).sup.2 I.sup.2 ∫(1/r.sup.2)2πr dr=μ.sub.0 (120.8).sup.2 πI.sup.2 ln(b/a)

so

    force≈0.0576 I.sup.2 Newtons

The area of the mouth of the waveguide is:

    π(0.105.sup.2 -0.0381.sup.2)=0.03 m.sup.2

Therefore the mean pressure drop is:

    (0.0576/0.03)I.sup.2 =1.92 I.sup.2 Pascals

This pressure drop occurs over the depth of fluid required for the Bfield to go to zero due to the eddies. This distance is on the order ofthree skin depths, or 0.12 meters. Therefore the resonator can produce apressure drop of 1.92 I² Pascals over 0.12 meters of fluid which isequivalent to 16 I² Pa/m.

The design of a conventional electromagnetic thruster is shown in FIG.22. The dimensions of the thruster channel are 0.33 meters by 0.33meters by 3.9 meters. The thruster uses 1000 A to produce 1333 N. Thepressure drop is therefore 1333/0.33² which equals 1.22×10⁴ Pascals.Over a 3.9 meters length this is equivalent to 3.14×10³ Pa/m. A lengthof 0.12 meters of electrode carries a current of 1000(0.12/3.9), or30.77 A. Applying this current in the embodiment of the inventiondescribed above would yield 16(30.77)² Pa/m, or 15.1×10³ Pa/m. Thus theembodiment of the invention described above is approximately 5 timesmore efficient that the conventional thruster. Furthermore, theinvention does not require a superconducting magnet to supply the Bfield.

As will be understood by those familiar with the art, the presentinvention may be embodied in other specific forms without departing fromthe spirit or essential characteristics thereof. Accordingly, disclosureof the preferred embodiment of the invention is intended to beillustrative, but not limiting, of the scope of the invention which isset forth in the following claims.

I claim:
 1. A pump, comprising:a length of a dielectric material formedinto a closed circuit; an open circuit of a lossy magnetic materialdefined by a length of said magnetic material and a gap, wherein a firstportion of said length of said magnetic material is wound around aportion of said length of said dielectric material; a conducting fluid,wherein said gap is immersed in said conducting fluid; a fluidredirection skirt at least partially surrounding said gap, wherein saidfluid redirection skirt has at least one fluid intake port and at leastone fluid exhaust nozzle; a solenoid wound around a second portion ofsaid length of said magnetic material; and an AC voltage sourceconnected to said solenoid.
 2. The pump of claim 1, wherein said fluidredirection skirt is substantially transparent to electromagnetic waves.3. The pump of claim 1, wherein said magnetic material has an imaginarypart of a complex permeability much greater than
 1. 4. The pump of claim1, wherein said magnetic material has an imaginary part of a complexpermeability within a range of about 1000 to about 5000 times apermeability of free space.
 5. The pump of claim 1, wherein saidmagnetic material has an imaginary part of a complex permeability withina range of about 10⁶ to about 5×10⁶ times a permeability of free space.6. The pump of claim 1, wherein said magnetic material has an imaginarypart of a complex permeability within a range of about 1 to about 5times a permeability of free space.
 7. A pump, comprising:a length of adielectric material formed into a closed circuit; an open circuit of alossy magnetic material defined by a length of said magnetic materialand a gap, wherein a first portion of said length of said magneticmaterial is wound around a portion of said length of said dielectricmaterial; a conducting fluid, wherein said gap is immersed in saidconducting fluid; a fluid redirection skirt at least partiallysurrounding said gap, wherein said fluid redirection skirt has at leastone fluid intake port and at least one fluid exhaust nozzle, whereinsaid fluid redirection skirt is fabricated of plastic; a solenoid woundaround a second portion of said length of said magnetic material; and anAC voltage source connected to said solenoid.
 8. A pump, comprising:alength of a dielectric material formed into a closed circuit; an opencircuit of a magnetic material defined by a length of said magneticmaterial and a gap, wherein a first portion of said length of saidmagnetic material is wound around a portion of said length of saiddielectric material; a conducting fluid, wherein said gap is immersed insaid conducting fluid; a fluid redirection skirt at least partiallysurrounding said gap, wherein said fluid redirection skirt has at leastone fluid intake port and at least one fluid exhaust nozzle; means forartificially causing said magnetic material to exhibit a high loss; asolenoid wound around a second portion of said length of said magneticmaterial; and an AC voltage source connected to said solenoid.
 9. Thepump of claim 6, wherein said fluid redirection skirt is substantiallytransparent to electromagnetic waves.
 10. The pump of claim 8, whereinsaid means is an external DC magnetic field applied to said magneticmaterial.
 11. A pump, comprising:a length of a dielectric materialformed into a closed circuit; an open circuit of a magnetic materialdefined by a length of said magnetic material and a gap, wherein a firstportion of said length of said magnetic material is wound around aportion of said length of said dielectric material; a conducting fluid,wherein said gap is immersed in said conducting fluid; a fluidredirection skirt at least partially surrounding said gap, wherein saidfluid redirection skirt has at least one fluid intake port and at leastone fluid exhaust nozzle, wherein said fluid redirection skirt isfabricated of plastic; means for artificially causing said magneticmaterial to exhibit a high loss; a solenoid wound around a secondportion of said length of said magnetic material; and an AC voltagesource connected to said solenoid.
 12. A method of pumping a conductivefluid, comprising the step of:applying an AC voltage to a solenoid woundaround a first portion of a length of a lossy magnetic material, saidlength of said magnetic material in combination with a gap defining anopen circuit, wherein a second portion of said length of said magneticmaterial is wound around a portion of a length of a dielectric materialformed into a closed circuit, said gap immersed within said conductivefluid, and wherein said conductive fluid enters a redirection skirt atleast partially surrounding said gap through at least one intake portand exits through at least one exhaust nozzle.